# module

## Primary tabs

Synonym:
left module, right module
Type of Math Object:
Definition
Major Section:
Reference
Groups audience:

## Mathematics Subject Classification

### correction of definition

The module definition does not require an identity element in the ring. Those satisfying 1 * m = m for all m in the module are called
unitary modules.
-- S.A. G.

### correction of typographicalerror of unital module

Left (right) R modules M for rings R with identity 1 such that 1 * m = m (m * 1 = m) for all m in M are call unital modules.
-- S. A. G.

### typographical correction of unital module

Left (right) R modules M for rings R with identity 1 such that 1 * m = m (m * 1 = m) for all m in M are called unital modules.
-- S. A. G.

### simplifying the definition

Properties 1 through 4 are just the propreties of an abelian group. Wouldn't it be simpler to say that a module is an abelian group (M,+) with a binary operation . : R x M -> M that satisfies properties 5 through 7?